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In this series, we will be examining the world of FreeCAD, an open-source CAD modeling application that is still in Beta, but has been gaining acceptance in recent years. Naturally, it is readily available in the Ubuntu repositories. In the ninth article on using FreeCAD, we used a 3D printer to create a physical representation of a construction. In this episode, we will explore some of the uses of copying objects to create a repetitive pattern such as chain-mail.
Dans cette série, nous examinerons le monde de FreeCAD, une application Open Source de modélisation par CAO qui est encore en bêta, mais qui a reçu un bon accueil ces dernières années. Naturellement, elle est facilement disponible dans les dépôts d'Ubuntu. Dans le neuvième article sur l'utilisation de FReeCAD, nous avons utilisé une imprimante 3D pour créer une représentation physique d'une construction. Dans cet épisode, nous explorerons certaines utilisations des copies d'objets pour créer des motifs répétitifs tels qu'une cote de maille.
Printing interlocking pieces Objects with repeated, but disjointed parts, such as chains or chain-mail, can be printed in 3D in much the same way as a regular, connected, part. The main difference is that the printer’s driver software should be smart enough to add in some extra plastic between bits. This is usually done in much the same way printers begin printing by laying down one or several mats on the bed, so as to ensure the parts being printed stick well to its surface, and do not move around as successive layers of plastic are added. In the adjoined image of a printer, two separate lengths of chain are being printed. In each case, the printer began with the mats, approximately 6 mm (a quarter-inch) out from the object’s outline. At this point, several layers of plastic have already been deposited, and the objects (chain links) are starting to appear. Excess plastic -among them, the diagonal traces and wavy bits- are also there, to ensure links stay upright and in a correct spatial relationship to each other.
L'impression de pièces imbriquées
LEs objets avec des éléments répétés mais disjoints, comme des chaînes ou une cote de maille, peuvent être imprimés en 3D de la même manière qu'une pièce normale, d'une seul tenant. La différence principale est que le logiciel pilote de l'imprimante doit être assez sophistiqué pour ajouter un peu de plastique supplémentaire entre les éléments. Ceci est fait en général d'une façon assez voisine à celle des imprimantes qui commencent par étaler un ou plusieurs tapis sur le support, de façon à assurer que les pièces sont bien collées à cette surface pendant l'impression et qu'elles ne bougent pas pendant l'ajout des couches successives de plastique. Dans l'image jointe d'une imprimante, deux longueurs séparées de chaîne sont en cours d'impression. Dans chaque cas, l'imprimante commence par les tapis, sur approximativement 6 mm sous le tracé de l'objet. Tel que sur l'image, plusieurs couches de plastique ont déjà été déposées et les objets (des maillons de chaîne) commencent à apparaître. Le plastique en trop - au milieu, les traces en diagonale et les petits bouts ondulés - sont aussi là pour assurer que les maillons restent en place et dans une position dans l'espace correcte entre eux.
Creating some chain Back to FreeCAD, let us begin by creating a very simple length of chain. We will start by doing a rectangular flat link, with a rectangular hole cut into it using the “cut” operation (Boolean volume subtraction). This link shape can be worked upon, and made rather more aesthetic or more functional, as desired. It is worth spending some time at this stage -perhaps rather more than I have done- since what we are producing here is a basic motif that will be repeated many times to create the complete chain object. Now, let us copy and paste our finished link. The new copy will need to be displaced a sufficient distance (e.g. along the X axis), and rotated by 90 degrees about the axis of displacement. Precise measurements will depend on link dimensions, but, in general, I do tend to leave, at the least, 1 mm of empty space between links. We now have something similar to this:
Créer une chaîne
Revenons à FreeCAD. commençons par créer une longueur de chaîne très simple. Nous commencerons par un maillon plat et rectangulaire, avec un trou rectangulaire pratiqué dedans en utilisant l'opération « cut » (soustraction booléenne de volumes).
Cette forme de maillon peut être retravaillée, pour la rendre plus esthétique ou plus fonctionnelle, suivant vos souhaits. Ça vaut le coup de passer plus de temps sur cette étape - peut-être plus que ce que j'ai fait - car ce que nous produisons ici est le motif de base qui sera répété de nombreuses fois pour créer un objet chaîne complet.
Maintenant, copions et collons notre chaînon fini. La nouvelle copie nécessitera d'être déplacée d'une distance suffisante (par ex., le long de l'axe x) et tournée de 90 degrés autour de l'axe du déplacement. Des mesures précises sont liées aux dimensions du maillon, mais, en général, j'ai tendance à laisser au moins 1 mm d'espace vide entre les maillons. Nous avons maintenant quelque chose qui ressemble à ça :
Now, for the weird part. In order to print this in 3D, we will need to move it out to the printer as one single object. But we already have defined two separate volumes, with some free air between them. So, now, we simply need to combine the two objects with a Boolean Union operation. This is really strange for someone with a mathematical background, since we are defining in essence a single volume with two separate and disconnected parts to it. But it does work. Once we have defined the couple of links as a single union object, we can now copy and paste that, obtaining two strings of two links. One of the strings needs to be displaced along the same axis into a suitable position, and then the two bits need to be fused to each other into a single Union object, as before. We can then continue in this fashion, multiplying the number of links by 2 in each operation: 1, 2, 4, 8, …
Maintenant, la partie bizarre. De façon à pouvoir l'imprimer en 3D, nous devons la sortir vers l'imprimante sous forme d'un objet unique. Mais nous avons déjà défini deux volumes séparés, avec un peu d'air libre entre eux. Aussi, maintenant, nous devons simplement combiner les deux objets avec une opération booléenne Union. Ceci est vraiment étrange pour quelqu'un qui a une formation mathématique, car nous définissons en fait un volume unique fait de deux éléments séparés et sans lien. Mais ça marche.
Une fois que nous avons défini la paire de maillons comme un unique objet union, nous pouvons maintenant le copier/coller, obtenant deux ensembles de deux maillons. l'un d'eux doit être déplacé sur le même axe dans une position adaptée, puis, ces deux ensembles doivent être fondus en un unique objet Union, comme précédemment. Nous pouvons continuer de cette façon en multipliant le nombre de maillons par deux à chaque opération : 1, 2, 4, 8, …
Once we have the workflow set out, we can experiment with more complex basic link forms. For instance, we could create a link with a flat eye and a vertical one. Thus, each successive copy can be displaced only along the axis, without any rotation. As before, the complete chain will need to end up as a single Union object, which can then be exported as an STL file and sent to the printer. It may be prudent to point out that the excess plastic will need to be pared away from the final object. This will include the mats set out beneath the chain, but also all the various bits and pieces the printer will have added to support the links, and also between each pair of links. A very complex link geometry may hinder getting all these bits out from our assembly. Practical experience shows that an object such as the above chain can take as long to clean up as to do the actual printing – if not more. Thinking ahead, and adjusting link shapes to make the interstitial spaces more easy to access, can be of help.
Spreading out to chain-mail Going from a linear piece of chain to flat chain-mail is not too complex. The main difficulty is that each link will need to be interlinked with many other links, typically four, so the central space will need to be created large enough to allow neighboring links to pass – while maintaining a separation of about 1 mm between any two links. As long as this is assured, links can take any form. One typical shape would be flat toroid rings (“donut-shaped”), set at different angles for each alternate row: a close-up of real mail can be seen at this link: https://en.wikipedia.org/wiki/Mail_(armour)#/media/File:European_riveted_mail_hauberk,_close_up_view.jpg. Other setups are also possible, for example curving each link into a saddle-shaped ring to aid fitment. Going even further in this direction, rounded links can be transformed into a collection of simple volumes (cylinders and bars), such as in the adjoining STL file (captured in Meshlab).
Once a basic link motif is created, it can be copied and pasted and separate links displaced into position. Then, several links can be fused into a single Union object, such as the above 8-link assembly, which is then repeated to create a larger piece of mail. Motifs can be added along two axis, to create a flat piece of material, or along one single direction to create a chain-mail band. Finally, chain-mail is not limited to square links or motifs in which links are connected to four other surrounding links. Three-sided symmetry can be used to create motifs in which triangular or hexagonal links are joined each to three other links. Links with a single ring can be alternated with links made of two parallel rings, joined by vertical parts that interlock with flat rings. This setup actually increases freedom of movement between links, producing a chain-mail fabric that folds and bends much better than a more traditional square motif.
What next? In this -final- article on using FreeCAD, we explored some of the uses of copying objects to create a repetitive pattern such as chain-mail. This could then be used as a basic material for different purposes, such as preparing costumes, historical recreations of armored clothing, or even rapid prototyping of jewelry. Going through the various articles that have come out over the last months, it is clear that a 3D design program such as FreeCAD has many different applications, ranging from mechanical engineering (gears), to architecture (buildings) and arts and crafts (chain-mail). It is always nice to see such software available for the various Ubuntu variants, where casual users benefit from free access to these applications, while more advanced users can use widely tested applications on a very stable platform. This is not always possible with commercial offerings that are often available for a very limited number of operating systems. After this review of some of the possibilities FreeCAD offers, this series of articles will go dormant for a time. Further along, it may be started up once more, if there is sufficient reader interest. Specific proposals would be very welcome.